मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Construct the truth table of the following: (∼p ∨ ∼q) ↔ [∼(p ∧ q)]

Advertisements
Advertisements

प्रश्न

Construct the truth table of the following:

(∼p ∨ ∼q) ↔ [∼(p ∧ q)]

बेरीज
Advertisements

उत्तर

p q ∼p ∼q ∼p ∨ ∼q p∧q ∼ (p∧q) (∼p ∨ ∼q) ↔ [∼ (p∧q)]
T T F F F T F T
T F F T T F T T
F T T F T F T T
F F T T T F T T
shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३३]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 6.2 | पृष्ठ ३३

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.

[~(~p ∧ ~q)] v q


Write down the following statements in symbolic form :

(A) A triangle is equilateral if and only if it is equiangular.
(B) Price increases and demand falls


Write the following compound statement symbolically.

Nagpur is in Maharashtra and Chennai is in Tamil Nadu. 


Write the following compound statement symbolically.

The angle is right angle if and only if it is of measure 90°.


Write the following compound statement symbolically. 

Hima Das wins gold medal if and only if she runs fast.


Construct the truth table of the following statement pattern.

(p ∧ ∼q) ↔ (p → q)


Construct the truth table of the following:

∼ (∼p ∧ ∼q) ∨ q


Determine the truth values of p and q in the following case:

(p ∨ q) is T and (p ∧ q) is T


Determine the truth values of p and q in the following case:

(p ∨ q) is T and (p ∨ q) → q is F


Write the negation of the following statement.

− 3 is a natural number.


Write the negation of the following statement.

2 + 3 ≠ 5


Write the truth value of the negation of the following statement.

`sqrt5` is an irrational number.


Write the following statement in symbolic form.

If triangle is equilateral then it is equiangular.


Write the following statement in symbolic form.

It is not true that “i” is a real number.


Write the following statement in symbolic form.

Milk is white if and only if the sky is not blue.


If p and q are true and r and s are false, find the truth value of the following compound statement.

(p → q) ↔ ~(p ∨ q)


If p and q are true and r and s are false, find the truth value of the following compound statement.

~ [p ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ q]


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement:

p ↔ ~ q


State whether the following statement is True or False:

The negation of 10 + 20 = 30 is, it is false that 10 + 20 ≠ 30.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

Mona likes Mathematics and Physics.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

If Kiran drives the car, then Sameer will walk.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

Even though it is not cloudy, it is still raining.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

It is not true that intelligent persons are neither polite nor helpful.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

If the question paper is not easy then we shall not pass.


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r :
Sachin is happy.
Write the verbal statement of the following.

(p ∧ q) ∨ r


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.
p→(q ∨ r)


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

∼ (p ∨ q) ∧ r


Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)

If price increases, then demand falls.


Write the negation of the following.

If ∆ABC is not equilateral, then it is not equiangular.


Rewrite the following statement without using the connective ‘If ... then’.

If it rains then the principal declares a holiday.


Find the negation of 10 + 20 = 30


Without using truth table prove that:

~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p


Write the following statement in symbolic form:

Milk is white if and only if the sky is not blue.


Write the following statements in symbolic form

If Kutab – Minar is in Delhi then Taj - Mahal is in Agra


Write the following statements in symbolic form

Even though it is not cloudy, it is still raining


Without using truth table show that -

(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)


If p : Every natural number is a real number.
q : Every integer is a complex number. Then truth values of p → q and p ↔ q are ______ and ______ respectively.


The symbolic form of the following circuit is (where p, q represents switches S1 and S2 closed respectively)


The negation of ∼s ∨ (∼r ∧ s) is equivalent to ______


The statement, 'If I go to school, then I will get knowledge' is equivalent to ______ 


Let S be a non-empty subset of R. Consider the following statement:

p: There is a rational number x ∈ S such that x > 0. Which of the following statements is the negation of the statement p? 


The logical statement (∼p → q) ∧ (q → p) is equivalent to: ______ 


Converse of the statement q `rightarrow` p is ______.


Construct the truth table for the statement pattern:

[(p → q) ∧ q] → p


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×